Cubic Interpolation (Interpolation, part II)

In a previous entry, we had a look at linear interpolation and concluded that we should prefer some kind of smooth interpolation, maybe a polynomial.

However, we must use a polynomial of sufficient degree so that neighboring patches do not exhibit very different slopes on either side of known points. This pretty much rules out quadratic polynomials, because polynomials of the form are only capable of expressing (strictly) convex (or concave) patches. A quadratic piece-wise function would look something like:

Wallpaper: Rust Matrix

(Rust Matrix, 1920×1200)

More wallpapers can be found here

Wallpaper: Stone Squid

(Stone Squid, 1920×1200)

More wallpapers can be found here

Wallpaper: Rocket to Mars

(Rocket To Mars, 1920×1200)

More wallpapers can be found here

Fast Fibonacci

The Fibonacci numbers are very interesting for many reasons, from seed heads to universal coding (such as Taboo Codes). Just figuring how to compute them efficiently is plenty of fun.

The classical formulation of the Fibonacci numbers is given by the following recurrence:

Linear Interpolation (Interpolation, part I)

In a couple of different occasions I discussed the topic of interpolation, without really going into the details. Lately, I had to interpolate data and that got me interested (again) in interpolation; and I think I should share some of the things I learned.

In this first post (of a series), let us begin by the simplest interpolation of all (after constant interpolation): linear interpolation.

Wallpaper: Self-Contained

(Self-Contained, 1920×1200)

Wallpaper: Spiral

(Spiral, 1920×1200)

Ambiguous Domain Names

Two weeks ago I attended the Hackreduce Hackathon at Notman House to learn about Hadoop. I joined a few people I knew (and some I just met) to work on a project where the goal was to extract images from the Wikipedia and see if we could correlate the popularity, as the number of references to the image, to some of the intrinsic images characteristics.

But two other guys I know (David and Ian) worked on a rather amusing problem: finding domain names that can be parsed in multiple, hilarious ways. I decided to redo their experiment, just for fun.

Faster Collatz

Quite a while ago, I presented the Collatz conjecture and I was then interested in the graphical representation of the problem—and not really going anywhere with it.

In this entry, let us have a look at the implementation of the Collatz function.